A CHARACTERIZATION OF ROOT CLASSES OF GROUPS

被引：21

作者：

Sokolov, E. V. ^{[1
]}

机构：

[1] Ivanovo State Univ, Dept Math & Comp Sci, Ivanovo 153025, Russia

来源：

COMMUNICATIONS IN ALGEBRA | 2015年 / 43卷 / 02期

关键词：

Generalized free product; Nilpotent group; Residual solvability; Root class of groups;

D O I：

10.1080/00927872.2013.851207

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a class of groups is root in a sense of K. W. Gruenberg if, and only if, it is closed under subgroups and Cartesian wreath products. Using this result we obtain a condition which is sufficient for the generalized free product of two nilpotent groups to be residual solvable.

引用

页码：856 / 860

页数：5

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